Out of Equilibrium Fields in Inflationary Dynamics. Density Fluctuations

Abstract

The energy and time scales during the inflationary stage of the universe calls for an out of equilibrium quantum field treatment. Moreover, the high energy densities involved (∼1/g ∼ 10¹²) make necessary the use of non-perturbative approaches as the large N and Hartree methods. We start these lectures by introducing the such non-perturbative out of equilibrium methods in cosmological universes. We discuss the renormalization procedure and the choice of initial conditions. We then study with these methods the non-linear dynamics of quantum fields in matter and radiation dominated FRW and de Sitter universes. For a variety of initial conditions, we compute the evolution of the inflaton, its quantum fluctuations and the equation of state. We investigate the phenomenon of explosive particle production due to spinodal instabilities and parametric amplification in FRW and de Sitter universes with and without symmetry breaking. We find that the particle production is somewhat sensitive to the expansion of the universe. In the large N limit for symmetry breaking scenarios, we determine generic late time fields behavior for any flat FRW and de Sitter cosmology. We find that quantum fluctuations damp in FRW as the square of the scale factor while the order parameter approaches a minimum of the potential at the same rate. We present a complete and numerically accessible renormalization scheme for the equation of motion and the energy momentum tensor in flat cosmologies. In this scheme the renormalization constants are independent of time and of the initial conditions. Furthermore, we consider an O(N) inflaton model coupled self-consistently to gravity in the semiclassical approximation, where the field is subject to ‘new inflation’ type initial conditions. We study the dynamics self-consistently and non-perturbatively with non-equilibrium field theory methods in the large N limit. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off the inflationary growth of the scale factor. We find that a very specific combination of these large fluctuations plus the inflaton zero mode assemble into a new effective field. This new field behaves classically and it is the object which actually rolls down. We show how this reinterpretation qualitatively saves the standard picture of how metric perturbations are generated during inflation and that the spinodal growth of fluctuations dominates the time dependence of the Bardeen variable for superhorizon modes during inflation. We compute the amplitude and index for the spectrum of scalar density and tensor perturbations and argue that in all models of this type the spinodal instabilities are responsible for a ‘red’ spectrum of primordial scalar density perturbations. The decoherence aspects and the quantum to classical transition through inflation are studied in detail by following the full evolution of the density matrix.